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If `a , b` are two fixed positive integers such that `f(a+x)=b+[b^3+1-3b^2f(x)+3b{f(x)}^2-{f(x)}^3]^(1/3)` for all real `x ,` then prove that `f(x)` is periodic and find its period.

A

a

B

2a

C

b

D

2b

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B
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OBJECTIVE RD SHARMA ENGLISH-REAL FUNCTIONS -Exercise
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  2. Let f be a real vlaued fuction with domain R such that f(x+1)+f(x-1)=s...

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  3. Let f be a real valued function with domain R satisfying f(x + k) =1+[...

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  4. The function f(x) given by f(x)=(sin 8x cos x-sin6x cos 3x)/(cos x cos...

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  5. If f(x) and g(x) are two real functions such that f(x)+g(x)=e^(x) and ...

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  6. Let f(x)=|x-2|+|x-3|+|x-4| and g(x)=f(x+1). Then :

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  7. If T(1) is the period of the function f(x)=e^(3(x-[x])) and T(2) is th...

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  8. Find the range of f(x)=sqrt(cos(sinx))+sqrt(sin(cosx)).

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  9. Find the domain of the function: f(x)=(sin^(-1)(x-3))/(sqrt(9-x^2))

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  10. If f: RvecR and g: RvecR are defined by f(x)=2x+3a n dg(x)=x^2+7, then...

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  11. Suppose f:[-2,2] to R is defined by f(x)={{:(-1 " for " -2 le x le 0...

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  12. If f:R->R and g:R->R is given by f(x) =|x| and g(x)=[x] for each x in ...

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  13. If a , b are two fixed positive integers such that f(a+x)=b+[b^3+1-3b^...

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  14. The domain of the function f(x)=(log)(3+x)(x^2-1) is (-3,-1)uu(1,oo) ...

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  15. Period of f(x)=sin3x cos[3x]-cos3x sin [3x] (where [ ] denotes the gre...

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  16. Let f(x)=(1)/(x) and g(x)=(1)/(sqrt(x)). Then,

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  17. Domain of (sqrt(x^(2)-4x+3)+1) log(5)""((x)/(5))+(1)/(x)(sqrt(8x-2x^(2...

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  18. The period of the function f(x)=cos2pi{2x}-sin2 pi {2x}, is ( w...

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  19. If f(n+2)=(1)/(2){f(n+1)+(9)/(f(n))}, n in N and f(n) gt0 for all n i...

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  20. Let f(x)={{:(x^(2) sin ((pix)/(2)),-1 lt x lt 1, x ne 0),(x|x|, x gt 1...

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